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slamgirl [31]
3 years ago
10

75,000 live bacteria are present in a culture in a flask. When an antibiotic is added to the culture, the number of live bacteri

a is reduced by half every four hours. Approximately how many hours have passed when there are 3000 bacteria left alive
Mathematics
1 answer:
Veronika [31]3 years ago
8 0
N = 75,000*(1/2)^(h/4) . . . . N = number alive; h = hours

3000 = 75000*(1/2)^(h/4) . . . . . substitute given numbers
1/25 = (1/2)^(h/4) . . . . . . . . . . . . . .divide by 75000
log(1/25) = (h/4)*log(1/2) . . . . . . . take the log, then divide by the coefficient of x
h = 4*log(1/25)/log(1/2) ≈ 18.6 . . . . hours

___
Of course log(1/25) = -log(25) = -2log(5), so the expression for h can be written as h = 8log(5)/log(2)
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